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Let   S   be a closed oriented surface of genus    g  ⩾  2   . Fix an arbitrary non‐elementary representation    ρ  :   π  1    (  S  )   →   SL  2    (  C  )and consider all marked (complex) projective structures on   S   with holonomy   ρ  . We show that their underlying conformal structures are dense in the moduli space of   S  .

Holonomy map fibers of ℂ P 1 ‐structures in moduli space